GeoGebras is a mathematical software platform that deals with algebra, graphing, calculus, linear functions, and basically anything else you can visualize using a function or equation. It began as a small university project but grew into an Open Source project. The software was designed for educational purposes and is meant for students of any age to use. This software has a number of advantages to it, the first being that it was programmed in Java and is usable, basically, on any operating system. The second primary advantage is that it is completely free for use, and does not even have to be downloaded onto the schools computers to be used as it can be run in just your web browser.
use spreadsheet data to chart coordinate positions with speed, date, and time
use colour, symbols and images to present information and data
make and justify problem solving decisions
estimate area of irregular shapes
find volume of geometric solids
find surface area of geometric solids
write and solve proportions
intersecting lines and planes
explore fractals
create geometric patterns
classify and draw mazes and labyrinths
develop deductive and inductive reasoning
What about the Mathematical Processes?
Technology is a given. Mental Math and Estimation can be used during interactive teaching and/or during private use. E.g. "Whats the midpoint of A and B?" Problem Solving can be used in lesson or assignments to discover ways of getting to a specific result. Such as "Using the given points A and B make equations for 3 same size circles. How about 4 similar Circles?" Visualization can be address along with Connections by allowing the students to see the pictorial side of their mathematics. Reasoning (inductive, deductive, proportional) and Inquiry can be addressed by using the software to derive conclusions from equations, figures, or both. It also allows students to make observations about any shape, line or polygon. Communication students, in an interactive lesson, have to describe discoveries and observations in a mathematical way.
Where in the Curriculum is GeoGebra useful?
WA10.8 Demonstrate an understanding of primary trigonometric ratios (sine, cosine, and tangent). WA10.9 Demonstrate understanding of angles including: • drawing and sketching • replicating and constructing • bisecting • relating to parallel, perpendicular, and transversal lines • solving problems. (From Workplace and Apprenticeship Mathematics 10 Saskatchewan Curriculum)
FP10.4 Develop and apply the primary trigonometric ratios (sine, cosine, tangent) to solve problems that involve right triangles. FP10.6 Expand and apply understanding of relations and functions including: • relating data, graphs, and situations • analyzing and interpreting • distinguishing between relations and functions. FP10.7 Demonstrate, with and without the use of technology, understanding of slope (concretely, pictorially, and symbolically) with respect to: • line segments and lines • rate of change • ratio of rise to run • parallel lines • perpendicular lines. FP10.8 Demonstrate understanding of linear relations including: • representing in words, ordered pairs, tables of values, graphs, function notation, and equations• determining characteristics including intercepts, slope, domain, and range • relating different equation forms to each other and to graphs. FP10.9 Demonstrate understanding of the writing and application of equations of linear relations, given: • a graph of a relation • a point that satisfies a relation and the slope of the relation • two distinct points that satisfy a relation • a point that satisfies the relation and the equation of a line parallel or perpendicular to the relation. FP10.10 Solve problems that involve systems of linear equations in two variables, graphically and algebraically. (From Foundations of Mathematics and Pre-calculus 10)
P9.2. Model and solve situational questions using linear equations of the form: ••ax = b ••= b, a ≠ 0 ••ax + b = c ••+ b = c, a ≠ 0 ••ax = b + cx ••a(x + b) = c ••ax + b = cx + d ••a(bx + c) = d(ex + f) ••= b, x ≠ 0 SS9.1 Demonstrate understanding of circle properties including: ••perpendicular line segments from the centre of a circle to a chord bisect the chord ••inscribed angles subtended by the same arc have the same measure ••the measure of a central angle is twice the measure of an inscribed angle subtending the same arc ••tangents to a circle are perpendicular to the radius ending at the point of tangency. [C, CN, PS, R, T, V] SS9.4 Demonstrate understanding of line and rotation symmetry. [C, CN, PS, V] (From Mathematics 9 Saskatchewan Curriculum)
Kojo Mathematics Software: Uses GeoGebra to futher their software into trigonometry, volumes, and geometric sequences.
GeoGebra Wiki: Here you will find many useful links and resources to further your use of GeoGebra software, including uses in Physics, Finances, Music, Art, Games and Puzzles, Statistics, and Geography.
What is it?
GeoGebras is a mathematical software platform that deals with algebra, graphing, calculus, linear functions, and basically anything else you can visualize using a function or equation. It began as a small university project but grew into an Open Source project. The software was designed for educational purposes and is meant for students of any age to use. This software has a number of advantages to it, the first being that it was programmed in Java and is usable, basically, on any operating system. The second primary advantage is that it is completely free for use, and does not even have to be downloaded onto the schools computers to be used as it can be run in just your web browser.How can I use GeoGebra in Math Education?
More specifically:
What about the Mathematical Processes?
Technology is a given.Mental Math and Estimation can be used during interactive teaching and/or during private use. E.g. "Whats the midpoint of A and B?"
Problem Solving can be used in lesson or assignments to discover ways of getting to a specific result. Such as "Using the given points A and B make equations for 3 same size circles. How about 4 similar Circles?"
Visualization can be address along with Connections by allowing the students to see the pictorial side of their mathematics.
Reasoning (inductive, deductive, proportional) and Inquiry can be addressed by using the software to derive conclusions from equations, figures, or both. It also allows students to make observations about any shape, line or polygon.
Communication students, in an interactive lesson, have to describe discoveries and observations in a mathematical way.
Where in the Curriculum is GeoGebra useful?
WA10.8 Demonstrate an understanding of primary trigonometric ratios (sine, cosine, and tangent).
WA10.9 Demonstrate understanding of angles including: • drawing and sketching • replicating and constructing • bisecting • relating to parallel, perpendicular, and transversal lines • solving problems. (From Workplace and Apprenticeship Mathematics 10 Saskatchewan Curriculum)
FP10.4 Develop and apply the primary trigonometric ratios (sine, cosine, tangent) to solve problems that involve right triangles.
FP10.6 Expand and apply understanding of relations and functions including: • relating data, graphs, and situations • analyzing and interpreting • distinguishing between relations and functions.
FP10.7 Demonstrate, with and without the use of technology, understanding of slope (concretely, pictorially, and symbolically) with respect to: • line segments and lines • rate of change • ratio of rise to run • parallel lines • perpendicular lines.
FP10.8 Demonstrate understanding of linear relations including: • representing in words, ordered pairs, tables of values, graphs, function notation, and equations• determining characteristics including intercepts, slope, domain, and range • relating different equation forms to each other and to graphs.
FP10.9 Demonstrate understanding of the writing and application of equations of linear relations, given: • a graph of a relation • a point that satisfies a relation and the slope of the relation • two distinct points that satisfy a relation • a point that satisfies the relation and the equation of a line parallel or perpendicular to the relation.
FP10.10 Solve problems that involve systems of linear equations in two variables, graphically and algebraically. (From Foundations of Mathematics and Pre-calculus 10)
P9.2. Model and solve situational questions using linear equations of the form: ••ax = b ••= b, a ≠ 0 ••ax + b = c ••+ b = c, a ≠ 0 ••ax = b + cx ••a(x + b) = c ••ax + b = cx + d ••a(bx + c) = d(ex + f) ••= b, x ≠ 0
SS9.1 Demonstrate understanding of circle properties including: ••perpendicular line segments from the centre of a circle to a chord bisect the chord ••inscribed angles subtended by the same arc have the same measure ••the measure of a central angle is twice the measure of an inscribed angle subtending the same arc ••tangents to a circle are perpendicular to the radius ending at the point of tangency. [C, CN, PS, R, T, V]
SS9.4 Demonstrate understanding of line and rotation symmetry. [C, CN, PS, V] (From Mathematics 9 Saskatchewan Curriculum)
Would you use this software? Please Explain
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Relevant Links
GeoGebra's Main Web Site
GeoGebra's Youtube Channel
MathPiper: Uses GeoGebra to make new programming software
Kojo Mathematics Software: Uses GeoGebra to futher their software into trigonometry, volumes, and geometric sequences.
GeoGebra Wiki: Here you will find many useful links and resources to further your use of GeoGebra software, including uses in Physics, Finances, Music, Art, Games and Puzzles, Statistics, and Geography.